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c
  . (7.36)
0
m

Taking into account that m Q g / (where g - acceleration
of gravity) and c  Q /  (where  - static deflection, which
corresponds to the equilibrium position of the beam), the
frequency of free vibrations can be represented as follows:
g
 0  . (7.37)

Sometimes it is convenient  to express movement 
0 11
1
through the action of the force. Since c the formula (7.36)

11
takes the form
1
  . (7.38)
0
 m
11
Formulas (7.36) - (7.38) calculate the angular frequency of
natural oscillations just as for longitudinal and torsional free
oscillations of elastic systems with one degree of freedom.

7.3.2 Forced oscillations beam with one degree of
freedom

Consider the case when attached to a weightless beam load
Q acting active periodic external force (fig.7.12).
The force that causes forced vibrations called perturbing
force. Simple forced vibrations occur under the action of
perturbing forces H (t ) , which varies according to the harmonic
law
H   Ht  sin  t , (7.39)
where H – greatest value perturbing forces;  – its circular
frequency.

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